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dc.contributor.authorJha, R.K.*
dc.contributor.authorUgail, Hassan*
dc.contributor.authorHaron, H.*
dc.contributor.authorIglesias, A.*
dc.date.accessioned2019-03-01T15:22:41Z
dc.date.available2019-03-01T15:22:41Z
dc.date.issued2018
dc.identifier.citationJha RK, Ugail H, Haron H et al (2018) Multiresolution discrete finite difference masks for rapid solution approximation of the Poisson's equation. In: 2018 12th International Conference on Software, Knowledge, Information Management & Applications (SKIMA). 3-5 Dec, Phnom Penh. Cambodia.en_US
dc.identifier.urihttp://hdl.handle.net/10454/16874
dc.descriptionYesen_US
dc.description.abstractThe Poisson's equation is an essential entity of applied mathematics for modelling many phenomena of importance. They include the theory of gravitation, electromagnetism, fluid flows and geometric design. In this regard, finding efficient solution methods for the Poisson's equation is a significant problem that requires addressing. In this paper, we show how it is possible to generate approximate solutions of the Poisson's equation subject to various boundary conditions. We make use of the discrete finite difference operator, which, in many ways, is similar to the standard finite difference method for numerically solving partial differential equations. Our approach is based upon the Laplacian averaging operator which, as we show, can be elegantly applied over many folds in a computationally efficient manner to obtain a close approximation to the solution of the equation at hand. We compare our method by way of examples with the solutions arising from the analytic variants as well as the numerical variants of the Poisson's equation subject to a given set of boundary conditions. Thus, we show that our method, though simple to implement yet computationally very efficient, is powerful enough to generate approximate solutions of the Poisson's equation.en_US
dc.description.sponsorshipSupported by the European Union’s Horizon 2020 Programme H2020-MSCA-RISE-2017, under the project PDE-GIR with grant number 778035.en_US
dc.language.isoenen_US
dc.relation.isreferencedbyhttps://doi.org/10.1109/SKIMA.2018.8631514en_US
dc.rights© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
dc.subjectPoisson's equationen_US
dc.subjectLaplace operatoren_US
dc.subjectAveragingen_US
dc.subjectFinite difference schemeen_US
dc.titleMultiresolution discrete finite difference masks for rapid solution approximation of the Poisson's equationen_US
dc.status.refereedYesen_US
dc.date.Accepted2018
dc.date.application2018
dc.typeConference paperen_US
dc.type.versionAccepted manuscripten_US
refterms.dateFOA2019-03-04T10:03:23Z


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